In this paper, a study on the fast numerical analysis based on spatial nonuniform grids and inverse problem for the two-dimensional space–time fractional coupled equations with fractional Neumann boundary conditions are conducted. The second order L1+ method combined with the Crank–Nicolson (CN) method in time and the fractional block-centered finite difference (BCFD) method based on spatial nonuniform

In real-world social and economic systems, the provisioning of public goods generally entails continuous interactions among individuals, with decisions to cooperate or defect being influenced by dynamic factors such as timing, resource availability, and the duration of engagement. However, the traditional public goods game ignores the asynchrony of the strategy adopted by players in the game. To address

In information visualization, the position of symbols often encodes associated data values. When visualizing data elements with both a numerical and a categorical dimension, positioning in the categorical axis admits some flexibility. This flexibility can be exploited to reduce symbol overlap, and thereby increase legibility. In this paper, we initialize the algorithmic study of optimizing symbol legibility

Cooperation is the foundation of social progress, but due to rational individuals often prioritize personal interests, reciprocal cooperation is undermined. The Public Goods Game (PGG) is a classic model for studying group interactions. Traditional PGG assumes a static environment, but in reality, the environment is dynamically changing, and there is an interaction between individual behavior and the

The stationary distribution, as a fundamental concept in stochastic processes, is of great significance for exploring the long-term behavior and stability of populations. In this paper, a stochastic reaction–diffusion predator–prey model with additional food, fear effect and anti-predator behavior is proposed, in which the stochastic fluctuations are characterized by a Ornstein–Uhlenbeck process. We

The dispersion error, also known as the pollution effect, is one of the main difficulties in numerical solutions to the wave propagation problem at high wavenumbers. The pollution effect, especially in mesh-based methods, can potentially be controlled by using either finer meshes or higher-order discretizations. Using finer meshes often leads to large systems that are computationally expensive to solve

Entropy and mutual information rates are key concepts in information theory that measure the average uncertainty and statistical dependence growth between two stochastic processes, respectively. This paper introduces a distance rate measure for discrepancy growth between two stationary processes, termed the Jensen-distance rate (JDR), which is based on spectral and cross-spectral densities. I examine

This paper deals with an inertial proximal algorithm that contains a Tikhonov regularization term, in connection to the minimization problem of a convex lower semicontinuous function f. We show that for appropriate Tikhonov regularization parameters the value of the objective function in the sequences generated by our algorithm converge fast (with arbitrary rate) to the global minimum of the objective

In this paper we introduce the concept of integral hypergraphs - hypergraphs whose all adjacency eigenvalues are integers, in analogy to integral graphs. We present infinite families of integral uniform hypergraphs, especially hypergraphs built by two operations, the s-extension of a graph and the k-power of a graph. Our main result is about integrality for uniform hypercycles, obtaining a characterization

This paper focuses on the Euler–Maruyama (EM) scheme for delay-type stochastic McKean–Vlasov equations (DSMVEs) driven by fractional Brownian motion with Hurst parameter H∈(0,1/2)∪(1/2,1). The existence and uniqueness of the solutions to such DSMVEs whose drift coefficients contain polynomial delay terms are proved by exploiting the Banach fixed point theorem. Then the propagation of chaos between

How to design control algorithms to effectively regulate the collective behavior with sensing delay remains a formidable challenge. In this paper, we propose to use bifurcation control with PD controller to regulate the collective behavior under sensing delay. The controlled system exhibits the emergence of three distinct states. Bifurcation analysis reveals that the Hopf bifurcation and pitchfork

This article concerns the following Klein–Gordon–Maxwell system −Δu+V(x)u−(2ω+ϕ)ϕu=|u|s−2u+λf(u),x∈R3,Δϕ=(ω+ϕ)u2,x∈R3,where ω>0 is a constant, 4≤s<6, λ>0 is a parameter. When f only satisfies suplinear conditions but not satisfies subcritical growth and Ambrosetti–Rabinowitz conditions, the existence of positive solution can be proved via variational methods, Moser iteration and perturbation arguments

This work addresses the development of a physics-informed neural network (PINN) with a loss term derived from a discretized time-dependent full-order and reduced-order system. In this work, first, the governing equations are discretized using a finite difference scheme (whereas any other discretization technique can be adopted), then projected on a reduced or latent space using the Proper Orthogonal

Aerosols, which are generated by the rupture of the liquid plug in the pulmonary respiratory tract, are important carriers of the viruses of infectious respiratory diseases, such as flu, tuberculosis, COVID-19, and Measles. In this study, we investigate liquid plug rupture and aerosol generation in the low respiratory tract with the alveolar structures by the chemical-potential multiphase lattice Boltzmann

A recently introduced coupling strategy for two nonconservative hyperbolic systems is employed to investigate a collapsing vapor bubble embedded in a liquid near a solid. For this purpose, an elastic solid modeled by a linear system of conservation laws is coupled to the two-phase Baer–Nunziato-type model for isothermal fluids, a nonlinear hyperbolic system with nonconservative products. For the coupling

This paper explores the mean-square bounded synchronization problem of leader-following multi-agent systems (LF-MASs) with directed graph under dual-channel stochastic switching deception attacks. Compared to previous studies, a new dual-channel stochastic switching deception attack mode is considered. Under this attack mode, the actuator receives different deception signals sourced from either the

Global optimization is a topic of great interest because of the many practical problems in real life. This article focuses on the unconstrained global minimization of multi-modal continuously differentiable functions, an important subclass of global optimization problems. In order to solve these problems, we develop a new global optimization technique that utilizes two fundamental concepts. The first

In cooperative systems, information exchange is essential for achieving consensus, and the preservation of data privacy has attracted growing attention. However, most existing studies have been limited to first-order multi-agent systems. This study investigates the privacy-preserving consensus problem of second-order agents with Lipschitz-type nonlinearities. A novel masking scheme based on specific

Consider the Neumann problem: −Δu−μ|x|2u+λu=|u|q−2u+|u|p−2uinR+N,N≥3,∂u∂ν=0on∂R+Nwith the prescribed mass: ∫R+N|u|2dx=a>0,where R+N denotes the upper half-space in RN, 1|x|2 is the Hardy potential, 20, ν stands for the outward unit normal vector to ∂R+N, and λ appears as a Lagrange multiplier. Firstly, by applying Ekeland’s variational principle, we establish the existence of normalized solutions that

This paper aims to discuss the existence, uniqueness and continuous dependence of mild solution of a class of non-autonomous stochastic neutral functional differential equations with state-dependent delay. Firstly, by using operator theory and estimates of the nonlinear term, we obtain the existence, uniqueness and continuous dependence of our concern system. Secondly, through the Arzelà–Ascoli theorem

This paper focuses on the research of nonlinear distributed parameter cyber physical systems (DP-CPS) via finite-time interval. The nonlinearity of the DP-CPS is captured through the utilization of the Takagi–Sugeno (T–S) fuzzy model, which gives rise to a class of fuzzy parabolic partial differential equation (PDE). In order to optimize the network resources, a class of dynamic quantizer is employed

Breast cancer remains one of the most prevalent and life-threatening diseases worldwide, necessitating mathematical modelling frameworks to capture the complexity of its progression and risk factors. This research endeavor uncovers the novel machine learning expedition using an Adaptive Nonlinear AutoRegressive eXogenous (ANARX) neural network on a Fractional Order Breast Cancer Risk (FO-BCR) model

The objective of this paper is to consider the asymptotical behavior of solutions for the two-dimensional partial dissipative Boussinesq system with memory and additive noise. We first establish the existence of a random absorbing set in the phase space. However, due to the presence of the memory term, we cannot obtain some kind of compactness of the corresponding cocycle through Sobolev compactness

We present a methodology for computing normal forms in discrete systems, such as those described by Poincaré maps. Our approach begins by calculating high-order derivatives of the flow with respect to initial conditions and parameters, obtained via jet transport, and then applying appropriate projections to the Poincaré section to derive the power expansion of the map. In the second step, we perform

Although many physical experiments and numerical simulations show that the magnetic field can stabilize and inhibit electrically conducting fluids, whether 2D incompressible MHD equations with only magnetic diffusion develop finite time singularities or not is one of the most challenging problems and remains open. Therefore, this issue has always attracted a lot of attention of mathematicians. Due

We consider a class of wave equations with strong damping, weak damping and nonlinear source term. By constructing the relationship between the blowup time and the coefficients of strong damping and weak damping, we exhibit and verify an interesting phenomenon that the local solution becomes the global solution as the coefficient of strong damping or weak damping goes to infinity.

In this paper, based on a novel integral inequality and the Lyapunov direct method, we propose a systematic approach to determining the global stability of the endemic steady states of age-structured epidemic models. The inequality makes it convenient to verify the negative (semi-)definiteness of the derivative of a Lyapunov functional candidate. The applicability of this approach is illustrated with

This paper focuses on a category of stochastic single population systems. Under mild assumptions, we provide a sufficient condition for the existence of stationary distribution in this system by employing variable substitution and the Krylov–Bogoliubov theorem. Furthermore, we demonstrate its proximity to being the sufficient and necessary condition by examining the system’s extinction.

SIAM Review, Volume 67, Issue 2, Page 213-255, May 2025. Abstract.The goal of multiobjective optimization is to identify a collection of points which describe the best possible trade-offs among the multiple objectives. In order to solve this vector-valued optimization problem, practitioners often appeal to the use of scalarization functions in order to transform the multiobjective problem into a collection

We define the reduced biquaternion tensor ring (RBTR) decomposition and provide a detailed exposition of the corresponding algorithm RBTR-SVD. Leveraging RBTR decomposition, we propose a novel low-rank tensor completion algorithm RBTR-TV integrating RBTR ranks with total variation (TV) regularization to optimize the process. Numerical experiments on color image and video completion tasks indicate the

A H1-Galerkin mixed finite element method (MFEM) is explored for solving the nonlinear Klein–Gordon equation, utilizing the lower-order bilinear element paired with the zero-order Raviart–Thomas element (Q11+Q10×Q01). The existence and uniqueness of the solutions for the discretized system are rigorously established. By exploiting the integral identity associated with the bilinear element, a superconvergence

This paper proposes a new approach for analyzing extinction conditions in multi-stage epidemic models, incorporating stochastic noises to account for sudden environmental or population-level changes that influence infection transmission. By utilizing an (n+1)-dimensional perturbed system that captures both gradual amelioration and proportional jumps, the research establishes sharp extinction criteria

Propagation problems of reaction fronts in viscous fluids are crucial in many industrial and chemical engineering processes. The interactions between the reaction properties and the fluid dynamics yield a complex and nonlinear model of Navier–Stokes equations for the flow with a strong coupling with two reaction–advection–diffusion equations for the temperature and the degree of conversion. To alleviate

In this article, we investigate the nonlinear spectral properties of the coupled third-order flow of the Kaup–Newell (TOFKN) system by formulating a local matrix ∂̄-equation with non-normalized boundary conditions and two linear constraint equations. Furthermore, we derive a coupled Kaup–Newell hierarchy with sources using recursive operator. By employing a specially designed spectral transformation

We show that the following nonlinear system of difference equations of interest xn(l)=al∏j=1,j≠lkxn−1(j)f(xn−1(1),…,xn−1(k)),n∈N,l=1,k¯,where k≥2, aj,x0(j)∈ℂ∖{0},j=1,k¯, and the function f:ℂk→ℂ is homogeneous of degree k−2, is solvable in a closed form considerably extending some results in the literature.

For numerical methods applied to singularly perturbed reaction-diffusion problems, the balanced norm has emerged as an effective tool. In this manuscript, we analyze supercloseness properties in the balanced norm for the nonsymmetric interior penalty Galerkin (NIPG) method on a Bakhvalov-type mesh. To achieve this, we construct a novel interpolant that combines the Lagrange interpolant and a local

We present a new discretization scheme to solve the stationary drift-diffusion equations based on the hybrid mixed finite element method. A convenient change of variables is adopted and the partial differential equations of the system are decoupled and linearized through Gummel's map. This gives rise to three equations that need to be solved in a staggered fashion: one of reaction-diffusion type (Poisson)

SIAM Review, Volume 67, Issue 2, Page 411-411, May 2025. A short discussion on stochastic calculus is given under the assumption that the fundamentals of probability theory are known to readers. Some related basic details on probability theory should have been included to make the book more self-contained. Further, analytic solutions of some stochastic differential equations (SDEs), which are used

SIAM Review, Volume 67, Issue 2, Page 408-411, May 2025. Optimal transport was originally invented by Gaspard Monge [“Mémoire sur la théorie des déblais et des remblais,” Mem. Math. Phys. Acad. Royale Sci., (1781), pp. 666–704] to model the problem of optimally mapping one distribution of mass onto another. This was later reformulated by Leonid Kantorovich as a well-posed linear program using the notion

SIAM Review, Volume 67, Issue 2, Page 406-408, May 2025. The 2024 Nobel Prize in Physics was awarded to John Hopfield and Geoffrey Hinton for their work on artificial intelligence and machine learning. The award has been somewhat controversial in the physics community and prompted some heated debates, since the only apparent use of physics is the Boltzmann distribution in the sampling function of the

SIAM Review, Volume 67, Issue 2, Page 405-406, May 2025. Big Data Analytics for Smart Transport and Healthcare Systems explores the praxis of data analysis for urban, human-focused datasets. Through a series of timely case studies, the authors demonstrate the need for interdisciplinary approaches to studying big data. This text, which covers topics ranging from flight status to the COVID-19 pandemic

SIAM Review, Volume 67, Issue 2, Page 404-405, May 2025. “Math is like a drag queen: marvelous, whimsical, at times even controversial, but never boring!” That it how the preface of Math in Drag begins. It is also an excellent description of the book. Math in Drag was authored by Kyne Santos, who often goes by Kyne. Kyne studied mathematics at the University of Waterloo and went viral teaching math

SIAM Review, Volume 67, Issue 2, Page 401-403, May 2025. It’s 7.30 am when my alarm wakes me up and I am greeted by my notifications. While eating breakfast, I watch videos YouTube recommends to me: sometimes news stories, sometimes my guilty pleasure of a new “Say Yes to the Dress” clip. On my way to campus, I play my daylist, a curated playlist from Spotify based on what I normally listen to on a

SIAM Review, Volume 67, Issue 2, Page 399-399, May 2025.

SIAM Review, Volume 67, Issue 2, Page 375-398, May 2025. Abstract.We present and discuss the Streeter–Phelps equations, which were the first river quality model. If the parameters are constants, then the model in its linear formulation can be solved explicitly. This reveals, however, that depending on parameters and initial data, the model might predict negative oxygen concentrations, which marks a

SIAM Review, Volume 67, Issue 2, Page 373-373, May 2025.

SIAM Review, Volume 67, Issue 2, Page 353-372, May 2025. Abstract.Over the past few decades, nonlocal models have been widely used to describe aggregation phenomena in biology, physics, engineering, and the social sciences. These are often derived as mean-field limits of attraction-repulsion agent-based models and consist of systems of nonlocal partial differential equations. Using differential adhesion

SIAM Review, Volume 67, Issue 2, Page 351-351, May 2025.

SIAM Review, Volume 67, Issue 2, Page 321-350, May 2025. Abstract.The X-ray transform is one of the most fundamental integral operators in image processing and reconstruction. In this paper, we revisit the formalism of the X-ray transform by considering it as an operator between reproducing kernel Hilbert spaces (RKHSs). Within this framework, the X-ray transform can be viewed as a natural analogue

SIAM Review, Volume 67, Issue 2, Page 319-319, May 2025.

SIAM Review, Volume 67, Issue 2, Page 256-317, May 2025. Abstract.In this review paper, we provide an overview of numerical methods used in the study of the Gross–Pitaevskii eigenvalue problem (GPEVP). The GPEVP is an important nonlinear Schrödinger equation that is used in quantum physics to describe the ground states of ultracold bosonic gases. The discretization of the GPEVP leads to a nonlinear

SIAM Review, Volume 67, Issue 2, Page 211-211, May 2025.

We showcase the utility of the Lagrangian descriptors method in qualitatively understanding the underlying dynamical behavior of dynamical systems governed by fractional-order differential equations. In particular, we use the Lagrangian descriptors method to study the phase space structure of the unforced and undamped Duffing oscillator when fractional-order differential equations govern its time evolution

This research presents a novel quantized fuzzy control technique based on Luenberger-like disturbance observer for a class of nonlinear delayed parabolic partial differential equation (PDE) systems, which are influenced by two distinct types of disturbances. To begin with, the PDE system is decomposed using the Galerkin approach, resulting in a finite-dimensional slow ordinary differential equation

This paper studies the exponential stabilization issue of memristive neural networks (MNNs) in the presence of denial-of-service (DoS) attacks by using an event-triggering scheme. Unlike the existing event-triggering strategies, not only does the devised resilient discontinuous event-triggering (RDET) scheme avoid the Zeno phenomenon and reduce network communication resource utilization, but can it

In this article, an energy dissipative Crank-Nicolson (C-N) type fully discrete nonconforming finite element method (FEM) is developed for the damped wave equation with cubic nonlinearity, and its unconditional superconvergence behavior is rigorously analyzed for the nonconforming EQ1rot element. By introducing an auxiliary variable p=ut, the problem is converted to a proper parabolic system, a new

Recovering an unknown signal from quadratic measurements has gained popularity due to its wide range of applications, including phase retrieval, fusion frame phase retrieval, and positive operator-valued measures. In this paper, we employ a least squares approach to reconstruct the signal and establish its non-asymptotic statistical properties. Our analysis shows that the estimator perfectly recovers

Inferring information diffusion networks plays a crucial role in social network analysis and various applications. Existing methods often rely on the infection times of nodes in diffusion processes to uncover influence relationships. However, accurately monitoring real-time temporal information is challenging and resource-intensive. Additionally, some approaches that do not utilize infection timestamps

Over the last decade, high-frequency oscillations (HFOs), very high-frequency oscillations (VHFOs), and ultra-fast oscillations (UFOs) have been proposed as possible biomarkers for epileptogenic zones in individuals with drug-resistant epilepsy. Despite considerable interest, the mechanisms responsible for producing such high frequencies, significantly surpassing the physiological limits of neuronal

The transport of regolith material has been confirmed by in situ exploration missions to asteroids like Itokawa, Ryugu and Bennu, providing evidences for the topographic evolution of these minor planets. This paper studies the migration of disturbed regolith materials across the asteroid surface from the viewpoint of nonlinear dynamics. We propose a simplified two-dimensional model that captures the